Finite Group Databasebeta

← C2×#13082236 #15660872

Subgroups — C2×#13082236 #15660872

Order 2816.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082236C2132yesmaximal, direct product factor
2C2×#10623115C213yesmaximal, complemented
3C2×#10623225C216yesmaximal, complemented
4C2×Q8×D44C211yesmaximal, characteristic, complemented
5C2×#10623107C212yesmaximal, complemented
6C2×#10623257C213yesmaximal, complemented
7C2×#10623259C213yesmaximal, complemented
8C2×#10623222C216yesmaximal, complemented
9C2×C4×#4343C213yesmaximal, complemented
10C2×C4×#4343C211yesmaximal, characteristic, complemented
11C2×C4×Q8×D11C212yesmaximal, complemented
12C2×C11×#557C211yesmaximal, characteristic, complemented
13C22×#4343C2213yes—
14C22×#4343C2211yescharacteristic
15C22×Q8×D11C2212yes—
16C11×#557C22116yescomplemented
17C2×C11×C4⋊Q8C2213yes—
18C2×C11×#125C2216yes—
19C2×C4×Q8×C11C2213yes—
20C2×C4×Q8×C11C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×#66999C2216yes—
23C2×Q8×Dic11C2213yes—
24C2×Q8×Dic11C2211yescharacteristic
25#10623259C22148yescomplemented
26#10623257C22148yescomplemented
27#10623225C22196yescomplemented
28#10623222C22196yescomplemented
29#10623115C22148yescomplemented
30#10623107C22132yescomplemented
31Q8×D44C22116yescomplemented
32C4×#4343C22116yescomplemented
33C4×#4343C22148yescomplemented
34C4×Q8×D11C22132yescomplemented
35C2×#66951C22112yes—
36C2×#66950C2216yes—
37C2×#66950C2216yes—
38C2×#66948C2216yes—
39C2×#66947C22112yes—
40C2×#66946C2213yes—
41C2×#66946C2216yes—
42C2×#66946C2211yescharacteristic
43C2×#66945C2216yes—
44C2×#66945C2213yes—
45C2×#66945C2216yes—
46C2×#66945C2213yes—
47C2×C4⋊C4×D11C2216yes—
48C2×#66943C2216yes—
49C2×#66940C2216yes—
50C2×#66928C2216yes—
51C2×C4×D44C2216yes—
52C2×C4×D44C2213yes—
53C2×C4×D44C2213yes—
54C2×C42×D11C2216yes—
55C2×C42×D11C2213yes—
56C2×#66922C2213yes—
57C2×C4×Dic22C2216yes—
58C22×Q8×C11C2313yes—
59C22×Q8×C11C2311yescharacteristic
60C2×#4343—28no—
61C2×#4343—224no—
62C2×#4343C23124yes—
63C2×#4343C2318yes—
64C2×Q8×D11—216no—
65C2×Q8×D11C23116yes—
66C22×D44C2313yes—
67C22×D44C2316yes—
68C22×D44C2311yescharacteristic
69C22×C4×D11C2312yes—
70C22×C4×D11C2316yes—
71C22×C4×D11C2313yes—
72C22×C4×D11C2313yes—
73C22×C4×D11C2316yes—
74C22×C4×D11C2313yes—
75C22×Dic22C2316yes—
76C11×C4⋊Q8C23124yes—
77C11×#125C23148yes—
78C4×Q8×C11C23116yes—
79C4×Q8×C11C2318yes—
80C4×Q8×C11C23124yes—
81C2×C11×C4⋊C4C2316yes—
82C2×C11×C4⋊C4C2316yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2313yes—
85C2×C11×C4⋊C4C2316yes—
86C2×C42×C11C2316yes—
87C2×C42×C11C2313yes—
88#66999C23148yes—
89Q8×Dic11C23124yes—
90Q8×Dic11C2318yes—
91C2×(C2×D11)⋊C4C2312yes—
92C2×(C2×D11)⋊C4C2316yes—
93C2×(C2×D11)⋊C4C2316yes—
94C2×(C2×D11)⋊C4C2316yes—
95C2×(C2×D11)⋊C4C23112yes—
96C2×C4⋊Dic11C2313yes—
97C2×C4⋊Dic11C2313yes—
98C2×C4⋊Dic11C2316yes—
99C2×C4⋊Dic11C2316yes—
100C2×Dic11⋊C4C23112yes—
101C2×C4×Dic11C2316yes—
102C2×C4×Dic11C2313yes—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2316yes—
105C2×C4×Dic11C2313yes—
106#66951C23196yes—
107#66950C23148yes—
108#66950C23148yes—
109#66948C23148yes—
110#66947C23196yes—
111#66946C2318yes—
112#66946C23124yes—
113#66946C23148yes—
114#66945C23148yes—
115#66945C23124yes—
116#66945C23148yes—
117#66945C23124yes—
118C4⋊C4×D11C23148yes—
119#66943C23148yes—
120#66940C23148yes—
121#66928C23148yes—
122C4×D44C23124yes—
123C4×D44C23124yes—
124C4×D44C23148yes—
125C42×D11C23124yes—
126C42×D11C23148yes—
127#66922C23124yes—
128C4×Dic22C23148yes—
129C2×#3482—111nomaximal, Sylow
130C23×D11C2413yes—
131C23×D11C2412yes—
132C2×Q8×C11—212no—
133C2×Q8×C11#4118yescomplemented
134C2×Q8×C11C24112yes—
135C2×Q8×C11C2414yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2416yes—
138C22×C4×C11C2413yes—
139C22×C4×C11C2411yescharacteristic
140C22×C4×C11C2413yes—
141C22×Dic11C2413yes—
142C22×Dic11C2411yescharacteristic
143C22×Dic11C2416yes—
144C22×Dic11C2411yescharacteristic
145#4343—296no—
146#4343—232no—
147Q8×D11—264no—
148C2×D44—224no—
149C2×D44—212no—
150C2×D44#4118yescomplemented
151C2×D44C24112yes—
152C2×D44C24124yes—
153C2×D44C2414yes—
154C2×C4×D11—28no—
155C2×C4×D11—212no—
156C2×C4×D11—224no—
157C2×C4×D11—224no—
158C2×C4×D11—212no—
159C2×C4×D11—212no—
160C2×C4×D11C2418yes—
161C2×C4×D11C24124yes—
162C2×C4×D11C24112yes—
163C2×C4×D11C24112yes—
164C2×C4×D11C24124yes—
165C2×C4×D11C24112yes—
166C2×Dic22—224no—
167C2×Dic22C24124yes—
168C11×C4⋊C4C24124yes—
169C11×C4⋊C4C24124yes—
170C11×C4⋊C4C2414yes—
171C11×C4⋊C4C24112yes—
172C11×C4⋊C4C24124yes—
173C42×C11C24124yes—
174C42×C11C24112yes—
175(C2×D11)⋊C4C2418yes—
176(C2×D11)⋊C4C24124yes—
177(C2×D11)⋊C4C24124yes—
178(C2×D11)⋊C4C24124yes—
179(C2×D11)⋊C4C24148yes—
180C4⋊Dic11C24112yes—
181C4⋊Dic11C24112yes—
182C4⋊Dic11C24124yes—
183C4⋊Dic11C24124yes—
184Dic11⋊C4C24148yes—
185C4×Dic11C24124yes—
186C4×Dic11C24112yes—
187C4×Dic11C2414yes—
188C4×Dic11C24124yes—
189C4×Dic11C24112yes—
190#3482—1132no—
191C2×#557D1111yescharacteristic, complemented
192C2×#556—113no—
193C2×#552—116no—
194C2×D4×Q8—111no—
195C2×#548—112no—
196C2×#547—113no—
197C2×#533—113no—
198C2×#529—116no—
199C2×C4×#41—111no—
200C2×C4×#41—113no—
201C22×C4×Q8—112no—
202C23×C11C2511yescharacteristic
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—26no—
206C22×D11—26no—
207C22×D11—26no—
208C22×D11C2×#4118yes—
209C22×D11C2516yes—
210C22×D11C2514yes—
211Q8×C11—224no—
212Q8×C11C2×#41116yescomplemented
213C2×C4×C11—212no—
214C2×C4×C11—24no—
215C2×C4×C11—26no—
216C2×C4×C11C2×#41112yes—
217C2×C4×C11C2×#4114yes—
218C2×C4×C11C2514yes—
219C2×C4×C11C25112yes—
220C2×C4×C11C2516yes—
221C2×C4×C11C2512yes—
222C2×C4×C11C2516yes—
223C2×Dic11—212no—
224C2×Dic11—22no—
225C2×Dic11—26no—
226C2×Dic112−1+414yes—
227C2×Dic11C2516yes—
228C2×Dic11C2512yes—
229C2×Dic11C25112yes—
230C2×Dic11C2512yes—
231D44—248no—
232D44—224no—
233D44C2×#41116yescomplemented
234C4×D11—248no—
235C4×D11—248no—
236C4×D11—224no—
237C4×D11—224no—
238C4×D11—216no—
239C4×D11—224no—
240Dic22—248no—
241C22×#41—113no—
242C22×#41—111no—
243C23×Q8—112no—
244#557C2×D11116yescomplemented
245#556—1148no—
246#552—1196no—
247D4×Q8—1116no—
248#548—1132no—
249#547—1148no—
250#533—1148no—
251C2×C4⋊Q8—113no—
252C2×C4⋊Q8C2×D1113yes—
253#529—1196no—
254C2×#126—1112no—
255C2×#125—116no—
256C2×#125C2×D1116yes—
257C2×#124—116no—
258C2×#123—1112no—
259C2×C22⋊Q8—116no—
260C2×C22⋊Q8—116no—
261C2×C22⋊Q8—116no—
262C2×#121—116no—
263C4×#41—1148no—
264C4×#41—1116no—
265C2×C4×Q8—111no—
266C2×C4×Q8—113no—
267C2×C4×Q8—1132no—
268C2×C4×Q8—116no—
269C2×C4×Q8—116no—
270C2×C4×Q8C2×D1112yes—
271C2×C4×Q8C2×D1111yescharacteristic
272C2×C4×Q8C2×D1113yes—
273C2×C4×D4—111no—
274C2×C4×D4—116no—
275C2×C4×D4—113no—
276C2×C4×D4—113no—
277C2×C4×D4—113no—
278C2×C4×D4—116no—
279C2×#117—113no—
280C2×#117—116no—
281C2×#117—113no—
282C2×#117—116no—
283C22×C4⋊C4—116no—
284C22×C42—116no—
285C22×C42—113no—
286C22×C11C22×#4112yes—
287C22×C11C22×#4112yes—
288C22×C11C2×2−1+412yes—
289C22×C11C2611yescharacteristic
290C2×D11—24no—
291C2×D11—24no—
292C2×D11—216no—
293C2×D11—26no—
294C2×D11—26no—
295C2×D11—26no—
296C2×D11—412no—
297C2×D11C22×#4118yes—
298C4×C11—212no—
299C4×C11—24no—
300C4×C11—26no—
301C4×C11C22×#41112yes—
302C4×C11C22×#4114yes—
303Dic11—212no—
304Dic11—26no—
305Dic11—22no—
306Dic11C2×2−1+414yes—
307C2×#41—1124no—
308C2×#41—118no—
309C2×#41—2224no—
310C2×#41—228no—
311C22×Q8—1116no—
312C22×Q8—116no—
313C22×Q8—2216no—
314C22×Q8C22×D1113yes—
315C22×Q8C22×D1111yescharacteristic
316C22×D4—111no—
317C22×D4—116no—
318C22×D4—113no—
319C23×C4—116no—
320C23×C4—116no—
321C23×C4—113no—
322C23×C4—113no—
323C23×C4—113no—
324C23×C4—112no—
325C4⋊Q8—1124no—
326C4⋊Q8C22×D11124yes—
327#126—1196no—
328#125—1148no—
329#125C22×D11148yes—
330#124—1148no—
331#123—1196no—
332C22⋊Q8—1148no—
333C22⋊Q8—1148no—
334C22⋊Q8—1148no—
335#121—1148no—
336C4×Q8—118no—
337C4×Q8—1124no—
338C4×Q8—1148no—
339C4×Q8—1148no—
340C4×Q8C22×D11116yes—
341C4×Q8C22×D1118yes—
342C4×Q8C22×D11124yes—
343C4×D4—118no—
344C4×D4—1124no—
345C4×D4—1148no—
346C4×D4—1124no—
347C4×D4—1124no—
348C4×D4—1148no—
349#117—1124no—
350#117—1148no—
351#117—1124no—
352#117—1148no—
353C2×C4⋊C4—113no—
354C2×C4⋊C4—1112no—
355C2×C4⋊C4—116no—
356C2×C4⋊C4—113no—
357C2×C4⋊C4—116no—
358C2×C4⋊C4—1148no—
359C2×C4⋊C4C22×D1116yes—
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C4⋊C4C22×D1113yes—
362C2×C4⋊C4C22×D1116yes—
363C2×C4⋊C4C22×D1116yes—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—116no—
366C2×C22⋊C4—116no—
367C2×C22⋊C4—116no—
368C2×C22⋊C4—1112no—
369C2×C42—113no—
370C2×C42—116no—
371C2×C42—116no—
372C2×C42—113no—
373C2×C42—111no—
374C2×C42—1148no—
375C2×C42—1124no—
376C2×C42C22×D1113yes—
377C2×C42C22×D1116yes—
378C2×C11#348214yescomplemented
379C2×C11C23×#4111yescharacteristic
380C2×C11C23×#4111yescharacteristic
381C2×C11C22×2−1+411yescharacteristic
382D11—28no—
383D11—46no—
384C24—112no—
385C24—113no—
386#41—2296no—
387#41—2232no—
388C2×Q8—212no—
389C2×Q8—1124no—
390C2×Q8—2264no—
391C2×Q8—2224no—
392C2×Q8#434318yescomplemented
393C2×Q8C23×D11112yes—
394C2×Q8C23×D1114yes—
395C2×D4—118no—
396C2×D4—114no—
397C2×D4—1124no—
398C2×D4—1112no—
399C2×D4—2224no—
400C2×D4—2212no—
401C22×C4—111no—
402C22×C4—111no—
403C22×C4—113no—
404C22×C4—116no—
405C22×C4—118no—
406C22×C4—1124no—
407C22×C4—1124no—
408C22×C4—1112no—
409C22×C4—1112no—
410C22×C4—1112no—
411C22×C4—228no—
412C22×C4—2212no—
413C22×C4—2224no—
414C22×C4—2224no—
415C22×C4—2212no—
416C22×C4—2212no—
417C22×C4C23×D1112yes—
418C22×C4C23×D1113yes—
419C22×C4C23×D1116yes—
420C22×C4C23×D1113yes—
421C22×C4C23×D1111yescharacteristic
422C4⋊C4—1112no—
423C4⋊C4—1148no—
424C4⋊C4—1124no—
425C4⋊C4—1112no—
426C4⋊C4—1124no—
427C4⋊C4C23×D11124yes—
428C4⋊C4C23×D1114yes—
429C4⋊C4C23×D11112yes—
430C4⋊C4C23×D11124yes—
431C4⋊C4C23×D11124yes—
432C22⋊C4—118no—
433C22⋊C4—1124no—
434C22⋊C4—1124no—
435C22⋊C4—1124no—
436C22⋊C4—1148no—
437C42—1112no—
438C42—114no—
439C42—1112no—
440C42—1124no—
441C42—1124no—
442C42C23×D11112yes—
443C42C23×D11124yes—
444C11C2×#348211yescharacteristic, complemented, Sylow
445C23—118no—
446C23—114no—
447C23—116no—
448C23—224no—
449C23—224no—
450C23—226no—
451C23—226no—
452C23—226no—
453C23C24×D1111yescharacteristic
454Q8—224no—
455Q8—2248no—
456Q8C2×#4343116yescomplemented
457D4—1116no—
458D4—2248no—
459D4—2224no—
460C2×C4—212no—
461C2×C4—24no—
462C2×C4—26no—
463C2×C4—114no—
464C2×C4—112no—
465C2×C4—116no—
466C2×C4—112no—
467C2×C4—1112no—
468C2×C4—2216no—
469C2×C4—2224no—
470C2×C4—2248no—
471C2×C4—222no—
472C2×C4—2212no—
473C2×C4—226no—
474C2×C4—2248no—
475C2×C4—2224no—
476C2×C4—2224no—
477C2×C4C2×#4343112yes—
478C2×C4#41×D1114yes—
479C2×C4C24×D1114yes—
480C2×C4C24×D1116yes—
481C2×C4C24×D11112yes—
482C2×C4C24×D1116yes—
483C2×C4C24×D1112yes—
484C22—118no—
485C22—224no—
486C22—224no—
487C22—2216no—
488C22—226no—
489C22—226no—
490C22—226no—
491C22—4412no—
492C22C22×#434312yes—
493C22C2×#41×D1112yes—
494C22D11×2−1+412yes—
495C22C25×D1111yescharacteristic
496C4—212no—
497C4—24no—
498C4—26no—
499C4—114no—
500C4—226no—
501C4—222no—
502C4—2212no—
503C4C22×#4343112yes—
504C4C2×#41×D1114yes—
505C2—228no—
506C2—446no—
507C2#1308223614yesdirect product factor
508C2C22×#41×D1111yescharacteristic
509C2C23×#434311yescharacteristic
510C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#557C2
socleC23×C11C25
hypercenterC2×#557D11
hypocenterC11C2×#3482
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#557

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13082236C2direct (N × H)
2. C2×#10623115C2semidirect
3. C2×#10623225C2semidirect
4. C2×Q8×D44C2semidirect
5. C2×#10623107C2semidirect
6. C2×#10623257C2semidirect
7. C2×#10623259C2semidirect
8. C2×#10623222C2semidirect
9. C2×C4×#4343C2semidirect
10. C2×C4×#4343C2semidirect
11. C2×C4×Q8×D11C2semidirect
12. C2×C11×#557C2semidirect
16. C11×#557C22semidirect
25. #10623259C22semidirect
26. #10623257C22semidirect
27. #10623225C22semidirect
28. #10623222C22semidirect
29. #10623115C22semidirect
30. #10623107C22semidirect
31. Q8×D44C22semidirect
32. C4×#4343C22semidirect
33. C4×#4343C22semidirect
34. C4×Q8×D11C22semidirect
133. C2×Q8×C11#41semidirect
150. C2×D44#41semidirect
191. C2×#557D11semidirect
212. Q8×C11C2×#41semidirect
233. D44C2×#41semidirect
244. #557C2×D11semidirect
378. C2×C11#3482semidirect
392. C2×Q8#4343semidirect
444. C11C2×#3482semidirect
456. Q8C2×#4343semidirect
507. C2#13082236direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130822362
C2×#106231152
C2×#106232252
C2×Q8×D442
C2×#106231072
C2×#106232572
C2×#106232592
C2×#106232222
C2×C4×#43432
C2×C4×Q8×D112
C2×C11×#5572
C2×#348211